Asymptotic sharpness of a Bernstein-type inequality for rational functions in H^{2}

Rachid Zarouf (1)

1 Mathématiques Fondamentales

A Bernstein-type inequality in the standard Hardy space H^{2} of the unit disc \mathbb{D}=\{z\in\mathbb{C}:\,\vert z\vert<1\}, for rational functions in \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D} is considered. Its asymptotic sharpness is proved as n tends to \infty and r tends to 1.

Mots clés: Bernstein type inequality; rational functions; hardy space

Domaines: Variables complexes [math.CV]

Rachid Zarouf. Asymptotic sharpness of a Bernstein-type inequality for rational functions in H^{2}. St. Petersburg Mathematical Journal, 2012, 23 (2), pp.152--166. ⟨hal-00460327v3⟩